[Pete]

Stick the door key in the door key hole and lock and unlock the door with the key.
That's how you shut down the OE alarm.

The factory alarm needs to see the after market alarm.
If your aftermarket alarm has an output momentary ground (-) you need to connect that to your green wire coming from the door key lock/unlock cylinder,needs to see a momentary ground so it thinks you stuck the key in the door key hole.
You can find the green wire from the bundle of wires coming thru the door to inside under the dash panel drivers side the way to make sure you have the correct wie get your test light put it to hot (+) and the other check the wire and cycle the door lock key light should light up everytime you cycle/unluck the key.

Usually aftermarket alarms should have a dome light output just make sure it's a ground (-)output.

If you need more info let me know.
Pete